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Abstract

We experimentally demonstrate spatiotemporal focusing of light on single nanocrystals embedded inside a strongly scattering medium. Our approach is based on spatial wave front shaping of short pulses, using second harmonic generation inside the target nanocrystals as the feedback signal. We successfully develop a model both for the achieved pulse duration as well as the observed enhancement of the feedback signal. The approach enables exciting opportunities for studies of light propagation in the presence of strong scattering as well as for applications in imaging, micro- and nanomanipulation, coherent control and spectroscopy in complex media.

Sample backside imaged at the second harmonic wavelength λ = 420nm. (a) Average image obtained from 200 images, each with a different randomly generated illuminating phase pattern. Several nanocrystals are visible in the field of view. (b) Image after wave front shaping. The feedback signal for the optimization was the average count rate in a square of 1μmx1μm around the position of the selected particle, indicated by the dashed square. Here, the feedback signal was enhanced by a factor of ηexp = 3.0 · 102.

Second harmonic auto-correlation (AC) measured on an individual nanocrystal at the backside of the sample. The graphs show the mean count rate in a 1μmx1μm square around particle position. In particular, the measurements for particle 5 are shown (see Table 1). (a) AC before wave front shaping. The data shows a 3:2:1 contrast ratio between the quickly decaying correlation of the coherent part of the speckle pulse followed by a slower decay of the incoherent part of the speckle pulse towards the background. The data is fitted according to that model of Eq. (2). The only free parameter of the fit is the thickness of the medium. (b) AC measured on nanocrystal at the backside of a slab of disordered silica after wave front shaping. The FWHM of the fit based on the AC of a sech2 shaped pulse is 168fs, indicating a pulse duration of the fundamental pulse of 109fs at the particle position.

Fourier analysis of the feedback signal as a function of phase φa per segment during a sequence of the wave front shaping experiment. The graph on the left (a) shows the squared amplitude of the first non-zero frequency Fourier component |FT1|2 calculated by Eq. (14), the graph on the right (b) depicts the second component |FT2|2. The distributions are used to determine the amplitude distribution of the contributing segments and the noise level (see sections 3.2.5 and 4.2).

Tables (1)

Table 1 Summary of the results of six wave front shaping experiments, each with a different particle visible in Fig. 2. The pulse duration τpulse is calculated from the Gaussian fit to the AC curve after optimization. The experimentally observed enhancement ηexp is calculated by the ratio of the average count rate in a 1μmx1μm square around the particle position after and before optimization. For each particle we calculated the enhancement ηmodel of the time-integrated SH according to our model, calculated by ηmodel = cτcαcrηcw. The theoretical enhancement of the SH in a hypothetical continuous wave experiment ηcw, is calculated based on the experimentally determined amplitude contribution. The factor cτ, which corrects the enhancement for speckle pulses, was calculated using Eq. (10), where the sample thickness to model 〈I(t)〉 is determined from the fits of the AC in Fig. 3(a). The particles 1–5 were all located in close vicinity, where we assume a constant thickness and an average value cτ = 0.12 was determined. Particle 6 was located on a different spot on the sample, where we obtained cτ = 0.17. The factors cα = 0.28 and cR = 0.57 include the polarization and the susceptibility tensor and the focal volume, respectively (see sections 3.2.3 and 3.2.4).

Metrics

Table 1

Summary of the results of six wave front shaping experiments, each with a different particle visible in Fig. 2. The pulse duration τpulse is calculated from the Gaussian fit to the AC curve after optimization. The experimentally observed enhancement ηexp is calculated by the ratio of the average count rate in a 1μmx1μm square around the particle position after and before optimization. For each particle we calculated the enhancement ηmodel of the time-integrated SH according to our model, calculated by ηmodel = cτcαcrηcw. The theoretical enhancement of the SH in a hypothetical continuous wave experiment ηcw, is calculated based on the experimentally determined amplitude contribution. The factor cτ, which corrects the enhancement for speckle pulses, was calculated using Eq. (10), where the sample thickness to model 〈I(t)〉 is determined from the fits of the AC in Fig. 3(a). The particles 1–5 were all located in close vicinity, where we assume a constant thickness and an average value cτ = 0.12 was determined. Particle 6 was located on a different spot on the sample, where we obtained cτ = 0.17. The factors cα = 0.28 and cR = 0.57 include the polarization and the susceptibility tensor and the focal volume, respectively (see sections 3.2.3 and 3.2.4).